Graphing and Writing Equations of Circles

Standard Form of a Circle Center is at (h, k) r is the radius of the circle

General Form of a Circle

General Form of a Circle Every binomial squared has been multiplied out. Every term is on the left side, equal to 0. Squared terms go first in alpha order.

EX 1 Write an equation of a circle with center (3, -2) and a radius of 4. k r

EX 2 Write an equation of a circle with center (-4, 0) and a diameter of 10. k

EX 3 Write an equation of a circle with center (2, -9) and a radius of . k r

Opposite signs! ( , ) 6 -3 Take the square root! Radius 5 EX 4 Find the coordinates of the center and the measure of the radius. Opposite signs! ( , ) 6 -3 Take the square root! Radius 5

5. Find the center, radius, & equation of the circle. The center is The radius is The equation is (0, 0) 12 x2 + y2 = 144

6. Find the center, radius, & equation of the circle. (1, -3) The center is The radius is The equation is 7 (x – 1)2 + (y + 3)2 = 49

7. Graph the circle, identify the center & radius. (x – 3)2 + (y – 2)2 = 9 Center (3, 2) Radius of 3     

Converting from General to Standard A needs to be 1. Divide if needed. Move the x terms together and the y terms together. Move E to the other side of the equals sign. Complete the square (as needed) for x. Complete the square(as needed) for y. Factor the left & simplify the right.

8. Write the standard equation of the circle. State the center & radius.

9. Write the standard equation of the circle. State the center & radius.

10. Write the standard equation of the circle 10. Write the standard equation of the circle. State the center & radius.

11. Write the general form of the equation of the circle.